1993

The story of the operator theory starts in 1992. At that time I was working as a postdoc for the “Netherlands Integrated Soil Research Programme” (Vrije Universiteit, Amsterdam, September 1992 to August 1993). I had just finished my PhD in ecotoxicology. The postdoc position involved writing an integration study of 21 PhD projects on soil pollution and was supervised by prof Nico van Straalen en Herman Eijsackers. To begin with, I wrote a fact sheet about every project. My goal in the report was to organise stress targets and effects on systems at different 'levels' of organisation (from molecules to ecosystems). To realise this, a stringent and consistent hierarchical ranking of targets for stress was needed. The literature offered many 'hierarchies', but their ranking seemed not strict enough. So I concluded that something new had to be developed. It was far from obvious how to do this. A first attempt at theoretic integration entitled “Ecotoxicology across the levels of ecological organisation” was sent to the advisory committee in mid-1993. This draft already hinted at using dimensions as an organising principle, stating that “all stress on ecological systems is a combination of the effects on the creation and destruction of ‘matter’ and ‘information’ in systems”. Around this time prof. Bas Kooijman allowed me to read a first draft of his book “Dynamic energy budgets in biological systems”. Near the end of 1993, the project’s advisory committee received a second draft report. Later that year I also enjoyed reading Kauffman’s book “The Origins of Order”, in which the catalytic hypercycle plays a major role. I was greatly inspired by the network of interactions of the hypercycle, as the abstraction of the recurrently connected enzyme network seemed to offer a method for delineating a limited system, and therewith could offer a step towards fixed organisational levels. An idea was born. Many basic scetches for the operator hierarchy were put to paper during the winter of 1993-1994. A big challenge was to learn to understand in terms of limited networks of interactions all the transitions between types of organisation. Figure 1 shows one of them. It illustrates that I used hypercycle-like limits to processes, in combination with 'shell-like' structural limits, for identifying subsequent groups of 'particle types', for example atoms,

Figure 1: The figure illustrates one of the first drawings of the operator hierarchy (spring 1994). Note that every level still included the same number of elements.

cells, and brains. The surrounding layer was later called the 'interface'. To elaborate this rough scetch required studying many new things outside biology, ranging from quarks to neural networks. This took quite a while. About this time Bart Happel introduced me to the astonishing world of technical (modular, recurrent) neural networks and the fractal inner space they show.

1994

In August 1994, a final report on the integration project was sent to the advisory committee with the title “Application of a hierarchical concept of ecosystem organisation in ecotoxicology”. The report included a part about the dynamic balance of toxicants in organisms and a part about targets, buffering and plasticity and the processes of assessment, diagnosis and prognosis. The advisory committee responded with disappointment because they had hoped for indications of “What is an acceptable toxin level?”. Instead, the report dealt with: When, Why, How, Related to what, and even So What? The report introduced the basic ideas of the ‘operator’ and ‘closure’: “Using closure of operations as a borderline between two hierarchical levels in the information evolution, the organisation shows four levels: the sub-atomary level, the level of atoms and molecules, the organic level, and the level of the consciousness”. Importantly, it was concluded that “… the repeating of an evolutionary pattern within the hierarchical levels appeared to be so eminent, that we have given the resulting hierarchy a central position in this study”. As I learned later, I had in part been rediscovering a classical ranking proposed by Pierre Teilhard de Chardin, who also distinguished particles (the systems that were 'formed' and 'centered') from all other systems. But for me there were no reasons to assume a highest level Omega, and I had found ways to offer more precise definitions of the particle concept.

1995

It was a great help to discuss the operator hierarchy with prof. Cajo ter Braak in January 1995 (his comments included a list of 92 suggestions and questions in the manuscript’s margins). By this time, the operator hierarchy had evolved into the scheme in Figure 2, a scheme in which the subsequent steps were much clearer than in Figure 1. Now, the steps in between of the

Figure 2: The operator hierarchy (march 2005).

hadron, the atom, the cell and the neural network organism (which I christened 'memon' to distinguish it from 'animal', because an animal could also be a unicellular) were elaborated in more detail. Figure 2 reads from left to right and from top to bottom. It was around this time, that I first read work of Turchin (1995) about 'quanta of evolution' and of Francis Heylighen (1990) about 'relational closure' as a basis for distinction making. I imagined that subsequent rounded-off, or 'closed', processes would allow defining the layers of the hierarchy of natural organisation I had in mind.

1996-2000

In 1996, while working at NERI (Denmark), I submitted the Lego-bricks paper together with prof. Nico van Straalen. After two years it was sent back unreviewed. Klaus Skovbo Jensen then re-introduced me to prof. Eigen’s hypercycles. In 1997, I was inspired by Lars Witting who kindly gave me a draft of his book “A General Theory of Evolution”. In 1998, Hans Løkke gave me the green light for three months of writing time to restyle the ecotoxicology manuscript. But after these months of hard work -- during which I stayed in a NERI guesthouse -- it appeared that I had again underestimated the complexity and quantity of the work. In 1999, the LEGO-bricks paper was published in World Futures, the journal of general evolution. And later that year, a new job came along at Alterra as the head of the functional biodiversity team.

2001

During the last months of 2001, prof. Diedel Kornet introduced me to her idea of “slots in state space” and gave me an interesting scheme of the natural levels including elementary particles, atoms, molecules, free-living cells, multicellular organisms and interbreeding communities. This scheme also contained the principle of internal organisation as a separate dimension. In 2001, the prediction paper was published in Acta Biotheoretica. The prediction of future operators then awoke the media’s warm interest because of the question: “Will robots dominate humanity?”

2008-2010

The 2008 the Analysing Hierarchy paper was published in Biological Reviews. In 2010, the Definition of Life paper was published by Foundations of Science. In June 2009, prof. Rolf Hoekstra invited me to a meeting in his office with prof. Eörs Szathmáry. After a short presentation of the operator hierarchy’s major ideas, Eörs made two very valuable comments. As far as he knew, the idea of first-next possible closure was a unique approach. He also indicated that using only interactions as a basis for first-next possible closure in the ‘three dimensions picture’ was presumably too restrictive. This was a wise remark. Based on the accepted publications, I considered the possibility of a second PhD. When speaking to prof. Nico van Straalen about this plan, he advised me to contact prof. Hub Zwart of the Radboud University Nijmegen. This resulted in a very pleasant contact and two month of writing time to finalise the project, which on 6 September resulted in my second PhD, which appeared as a book in the Alterra Scientific contributions series nr. 34. For those that are curious about the cover picture, it refers to several ideas: 1. There is closure within the marble, which hints at closure as a basis for hierarchy, 2. The marble and the lines in it hint at structural and functional closure, 3. One can see a world (the cosmos and the operator hierarchy) in this 'grain of sand' (after all a marble is plain silicium), 4. The mable embodies the idea that closure allows for stringent type limits, just as sharp as the limit of a marble, 5. The operator theory with its stingent levels all the way op, turns the chaotic 'wood' of matter-energy, as Einstein called it, into 'marble'.

2011-2012At the start of 2011 a large new project came along, which was initiated by Frank Veeneklaas. The goal was to find scientific argumentation about why we should worry about the loss of biodiversity. Clearly, before one can answer this question, one needs to define biodiversity. In turn this implies defining what is 'bios' (thus 'life'). A long standing question had to be solved. I had shown in 2010 that the operator hierarchy can be used for defining life as a generic property that can be found in all organisms. And that an organism can be defined as an object which complies with the organisation that is defined by the operator types from the level of the cell (as an operator type) and up. On this basis, biodiversity was defined as the diversity of all organisms. If one focuses on the diversity of individuals, the current practices, which focus on genes, species and ecosystems, seem to neglect the complexity of neural networks. The consequences of this neglect are far reaching, because a simple calculation shows that the potential diversity of every human brain is astronomically large, when it is compared to the potential diversity of the human genome. This work resulted in the publication of "The pursuit of complexity".

2012-2014
In this period I have been working on the application of the operator theory for extending the evolution theory of Darwin.